Abstract

The dynamic response of filament wound cylindrical

composite structures subjected to underwater

impulsive loads is analyzed. The analysis focuses on

the effect of varying structural attributes and

material properties on load-carrying capacity,

deflection, energy dissipation and damage. The

structural designs studied are monolithic composite

structures and sandwich structures with foam cores

of different relative densities and different radii.

Underwater impulsive loads are generated using a

novel experimental setup. The deflection and core

compression are characterized using 2D Digital

Image Correlation (DIC). The experiments are

supported by fully dynamic numerical calculations

which account for fluid-structure interactions and

damage and failure mechanisms in the materials. For

the same applied impulse, the monolithic cylindrical

sections experience significant warping,

delamination and cracking, while the sandwich

structures experience significantly lower levels of

damage. In the sandwich structures, as the core

density increases, the transmitted impulse and

overall damage also increase. Deflection and

warping in the impulsively loaded region are

influenced by the radius of curvature and material

orientation. The results show that cylindrical

sandwich structures have superior blast-resistance

than cylindrical monolithic structures of equal mass

with only relatively minor increases in wall

thickness. The experiments, computations and

structure-performance relations obtained offer

approaches for designing structures with superior

blast mitigating capabilities for sections in critical

parts of ship structures like the keel, hull and pipes.

1. Introduction

Marine structures are designed to operate in hostile

environments which involve corrosive sea water, hot

and cold temperature extremes, transient dynamic

loads like hull slamming, and complex three

dimensional hydrodynamic load triaxialities.

Additionally, naval structures are required to

withstand weapons impacts and blast loads resulting

from surface and underwater explosions. Recent

assessments of marine structures have demonstrated

that sandwich composites can provide good blast

mitigation due to their high strength to weight ratios

and high shear and bending resistances.

Characterization of the behavior of composite

materials and polymeric foams under impulsive

loading is a prerequisite for the analysis and design

of effective, blast resistant sandwich composites.

Deformation and failure due to dynamic loading in

layered materials such as composite laminates has

been the subject of numerous investigations in recent

years. Gas gun based impact loading has been

successfully used to generate impulsive loading

through water [1-3]. A major of aspect of marine

composite structures that has not been thoroughly

investigated is the response of cylindrical composite

structures to blast loads. The objective of the present

work is to characterize the dynamic deformations

and damage response of curved sandwich

composites with different core densities but similar

total masses subjected to high intensity underwater

impulsive loads. The analysis focuses on the effect

of varying structural attributes and material

properties on load-carrying capacity, deflection,

energy dissipation and damage.

RESPONSE OF CYLINDRICAL COMPOSITE STRUCTURES

TO UNDERWATER IMPULSIVE LOADING

S. Avachat, M. Zhou*

George W. Woodruff School of Mechanical Engineering

School of Materials Science and Engineering

Georgia Institute of Technology, Atlanta, GA, USA

*Corresponding author (min.zhou@me.gatech.edu)

Keywords: Underwater blast loading, high-speed digital imaging, sandwich composites,

cylindrical structures, failure modes, cohesive finite element modeling

Keywords: keywords list (no more than 7)

This is a combined experimental and computational

study. Computationally, the cohesive finite element

method (CFEM) is employed to track the fracture

processes. The major fracture mechanisms

considered include interlaminar delamination

between composite plies with different fiber

orientations, intralaminar cracking, core cracking

and core-face debonding. In the CFEM framework,

there are two main approaches to resolve crack

initiation and growth. One approach is to insert

cohesive elements ahead of the crack tip as the crack

grows [4]. This method can avoid the cohesive

surface induced stiffness reduction of the overall

model caused due to a finite stiffness of the cohesive

traction-separation relation. However, this approach

is computationally expensive and requires specific

fracture initiation criteria. Another approach

involves embedding cohesive surfaces along all

finite element boundaries as an intrinsic part of the

physical model [5, 6]. The constitutive behavior of

bulk phases and cohesive surfaces are specified

separately. Dynamic crack initiation and growth can

be tracked using this framework. Additionally,

proper choice of cohesive surface stiffness and finite

element size can alleviate and minimize the cohesive

surface induced stiffness reduction [7].

2. Experimental facility and diagnostics

Planar underwater impulses are generated using a

novel experimental setup called the Underwater

Shock Loading Simulator (USLS). The USLS

consists of a projectile impact based impulsive

loading mechanism and clamped and simply

supported boundary conditions. The cylindrical

structure is supported on a steel flange. This loading

condition closely resembles that found in naval

structures. A force transducer is mounted on the

flange to measure impulses transmitted. The location

of material failure in this configuration allows

accurate time-resolved measurements using high-

speed digital imaging. Specifically, high-speed

digital imaging and digital image correlation enables

the study of deflection, face wrinkling, core face

debonding, core compression, core shear cracking

and rupture and their dependence on load intensity

and core characteristics. This experimental setup is

shown in Fig. 1.

The USLS can generate impulsive loads with peak

pressures within the range of 40-250 MPa, which

resembles those created by underwater explosions.

Fig. 2 shows the pressure histories of underwater

impulses corresponding to different projectile

velocities.

Water

High-Speed

Camera

Flash

Light

Projectile

Steel

Anvil

Support

Sandwich

Structure

Extension

Flash

Light

Flyer-plate

Fig. 1 Sectional view of Underwater Shock Loading

Simulator (USLS) showing the setup for high speed

digital imaging and digital image correlation

analysis of the response of impulsively loaded

cylindrical sandwich structures.

0

50

100

150

200

0 0.2 0.4 0.6 0.8 1

Time (ms)

Pre

ssure

(M

Pa)

V0= 100 m/s

V0= 80 m/s

V0= 50 m/s

V0= 30 m/s

Fig. 2 Measured experimental pressure histories in

the water chamber for four different projectile

velocities.

3. Materials

The composite specimens are constructed with glass

fiber reinforced plastic with two winding angles

[45o] and [-45

o]. The wall thickness of monolithic

cylindrical specimens is 5.5 mm. For the sandwich

structure, the outer face is 3.5 mm thick, the inner

face is 2.5 mm thick and the sandwich core is 10

mm thick. The core material is Divinycell HP100

PVC foam manufactured by DIAB Inc. [8]. Fig. 3

shows the different components of a filament wound

composite cylinder. The sandwich structure is

manufactured by cutting the PVC foam into the

required segments, inserting into concentric

composite cylinders and impregnating the assembly

with polyester resin. The inside surfaces of the

cylindrical specimens are painted with an enamel

spray to improve reflectivity for high-speed

photography.

Monolithic Cylindrical

Composite StructureSandwich Cylindrical

Composite Structure

Resin coat

Chopped strand mat

Structural layer

(+ 45)

Structural layer

(- 45)

Resin coat

Filament wound

fiberglassHP100

Fig. 3 Components of filament-wound, cylindrical

fiberglass structure with [45o]/[-45

o] orientations.

4. Numerical Modeling

Finite element simulations using the experimental

conditions and independently measured material

properties are conducted to support the experiments

and gain insight into the response of the structures.

The simulations account for the FSI effect at the

water composite interface, shear cracking and

fragmentation in the core, matrix cracking and fiber

failure in the faces, and core face interfacial

debonding. Both the bulk composite and PVC foam

follow an isotropic linear elastic constitutive

relation. Cohesive elements are specified between all

bulk element boundaries in the glass-reinforced

polyester as well as PVC foam. The cohesive

elements allow for damage initiation and

development. For the zero-thickness cohesive

elements, a bilinear cohesive law is adopted to

govern traction-separation behavior. A schematic

representation of the bilinear traction–separation law

is shown in Fig. 4. Loading initially proceeds from

point A to B, at which point softening occurs with

increasing strain until failure at a separation of δ.

Because it is not physically meaningful for

compressive tractions to contribute to damage

initiation, only tensile normal tractions are

considered in the damage initiation rule. Damage

initiated and failure in the interfaces follow the

mixed-mode fracture criterion [9]. Details about the

CFEM approach presented here can be found in [5,

7, 10].

After failure of the cohesive elements, contact

between bulk elements leads to frictional sliding.

The surfaces that are fractured are identified as

potential contact regions and master and slave

surface designations are assigned to the

corresponding bulk element faces. When the

surfaces come in contact with one another, the

Coulomb friction law governs the interfacial

frictional force. The coefficient of friction is 0.6,

which is typical for composite sliding [11].

CFEM models with cohesive traction-separation

behavior with finite initial stiffness have two

competing requirements on element size. The upper

bound requires that the element size must be small

enough to accurately resolve stress distribution

inside cohesive zones at crack tips. The lower bound

requires the cohesive surface induced stiffness

reduction be minimal such that wave speed in the

solid is not significantly affected. For the current

analysis, the element size 50 µm and is calculated

using the criteria specified in [7].

A

B

C

Pσmax

δ0 δul δ

Fig. 4 Bilinear traction-separation law for cohesive

elements.

A Lagrangian formulation is adopted to simulate

wave propagation in water. It captures the

exponentially decaying pressure waves and

cavitation at the fluid structure interface. The

response of water is described by the Mie-Gruneisen

equation of state.

5. Results

5.1 Experimental results

Structural attributes, loading intensities and

constituent properties determine the overall fracture

behavior through the activation of different fracture

mechanisms which include delamination,

interlaminar crack growth, intralaminar cracking,

core-face debonding and fragmentation. In response

to the impulsive loads specified in Fig. 2, a stress

wave propagates through the curved composite

laminate. The stress wave propagation is initially

perpendicular to incident wave and follows the

curvature of the cylindrical structure. Fig. 5 shows

high speed photographs of a monolithic composite

cylinder 5 mm in thickness subjected to an

underwater impulsive load corresponding to a

projectile velocity of 50 m/s. The high-speed

photographs capture the dynamic deformation and

warping in the composite cylinder. Figure 6 shows

the post-test photographs of loaded specimens.

Visual inspection reveals that delamination and fiber

and matrix rupture are the major failure mechanisms

in the cylindrical monolithic composite structure.

Delamination is observed through the thickness in

the filament wound plies while fiber and matrix

cracking is observed on the inner and outer surfaces

of the composite. For a similar incident impulse, the

monolithic cylindrical sections experience

significantly greater warping, delamination and

cracking as compared to sandwich structures. In

sandwich structures, the presence of a PVC foam

core provides resilience and flexural stiffness and

enhances the blast resistance of the structure and

consequently, reduces delamination and interlaminar

cracking. On the impulse side, the outer face

experiences interlaminar cracking and fiber-matrix

debonding and the inner face is relatively

undamaged. Permanent core compression is not

extensive and is restricted to the HP100 foam close

to the loaded area.

Overall, the following damage modes are observed

in both structures:

delamination and interlaminar cracking

intralaminar cracking, matrix cracking and

fiber rupture

structural deformation and warping

core compression and partial recovery.

100 µs 200 µs 300 µs 400 µs

500 µs 600 µs 700 µs 800 µs

900 µs 1000 µs 1100 µs 1200 µs

1300 µs 1400 µs 1500 µs 1600 µs

Figure 5 High speed photographs of a monolithic composite structure subjected to an impulsive load generated

by a projectile velocity of 0V =50 m/s .

Side-viewImpulse side Support side

76 mm

20

mm20

mm

100 mm 100 mm

Figure 6 Post-mortem photographs of impulsively loaded cylindrical composite structure. Delamination and

matrix cracking can be observed. The delaminated region is outlined in the impulse and support side pictures.

Side-viewImpulse side Support side

91 mm

20

mm20

mm

100 mm100 mm

Figure 7 Post-mortem photographs of an impulsively loaded cylindrical sandwich composite structure. The

delaminated region is outlined in the impulse and support side pictures. The areas of delamination on the

impulse and support sides as well interlaminar cracking are both significantly smaller in the sandwich structure.

5.2 Validation of numerical model

Results from the numerical analysis of the response

of the cylindrical composite structures to localized

blasts provides insight and a more in-depth

understanding of the failure modes, damage

initiation and growth, velocity transfer and energy

dissipation. The cohesive finite element framework

provides a means of evaluating the blast resistance

of composite structures though explicit simulation of

deformation processes in the structure. The

boundary conditions applied to the model represent

those in the experiments. The conditions closely

resemble a cylindrical structure anchored to a larger

structure, which is common for submarines,

underwater pipelines and missiles. As in

experiments, a planar underwater impulsive wave is

incident on the side of the cylinder simulating a

"side-on" loading condition.

Figure 8 shows the stress wave propagation in a

monolithic cylindrical composite structure. Figure 9

shows a sequence of magnified images illustrating

the damage initiation and growth process. As the

stress wave propagates through the composite

structure, the bonds between successive laminates

fail and delamination occurs at =200 μst . When the

interlaminar crack jumps from one interface to

another, it inevitably leads to matrix cracking and

intralaminar crack growth. Due to the dynamic

nature of this process, buckling initiates in the

composite structure and causes cracking and failure

in the laminates as observed at =600 μst . As

deformation progresses, the intralaminar cracks link

together to create a shear band along which the

entire laminate undergoes failure and rupture.

Figure 10 shows a comparison of experimentally

measured and computationally predicted

displacement and velocity profiles of the inner

surface of an impulsively loaded monolithic

composite cylinder. The simulation predicts a lower

value of permanent displacement and velocity but

the final value is within 5% of the experimentally

measured value.

200 µs 400 µs

600 µs 800 µs

1000 µs 1200 µs

1400 µs 1600 µs

50

mm

σ (MPa)

400

350

300

250

200150

100

75

50

255

0

Figure 8 Stress wave propagation, deformation and failure in a cylindrical monolithic composite structure at

different times.

7

RESPONSE OF CYLINDRICAL COMPOSITE STRUCTURES TO

UNDERWATER IMPULSIVE LOADING

200 µs 300 µs 400 µs 500 µs

600 µs 700 µs 800 µs 900 µs

1000 µs 1100 µs 1200 µs 1300 µs

Figure 9 Damage initiation and growth in cylindrical composite structure under impulsive loading.

Delamination initiates at =200 μst , and buckling occurs at = 400 μst . At = 600 μst , kinking occurs at the

inner surface and causes cracking followed by rupture and fragmentation.

0

20

40

60

80

100

0 100 200 300 400 500 6000

5

10

15

20

25

30

35

0 100 200 300 400 500 600

Time (µs)

Dis

pla

ce

me

nt (m

m)

Simulation

Monolithic

(Inner face)

Experimental

Time (µs)

Ve

locity (m

/s)

Monolithic

(Inner face)

Simulation

Experimental

Figure 10 Comparison of experimentally measured and computationally predicted displacement and velocity of

the inner face in a monolithic cylindrical composite subjected to an impulsive load corresponding to V0 = 50m/s.

5.3 Numerical results

The time histories of energy dissipation in the

monolithic structure are shown in Figure 11(a-c).

Dynamic compression in the bulk composite is the

primary dissipation mechanism in the earlier stages

of deformation, as the matrix absorbs the input

energy and accommodates the imposed deformation.

Accordingly, delamination initiates soon after the

onset of the impulsive load as the interlaminar

interfaces fail due to shear stresses. The failed

surfaces interact with each other causing friction.

The frictional dissipation in the structure is initially

significantly lower than fracture work but as the

fracture surfaces interact with each other, frictional

dissipation surpasses both strain energy as well

0

10

20

30

40

50

60

70

80

90

0 100 200 300 400 500 600

0

20

40

60

80

0 100 200 300 400 500 600

0

20

40

60

80

0 100 200 300 400 500 600

Time (µs)

En

erg

y (J)

Frictional

dissipation

En

erg

y (J)

Fracture

work Strain

energy

(a) Total

Time (µs)

En

erg

y (J)

Time (µs)

(b) Fracture work (c) Frictional dissipation

TotalTotal

Interlaminar

(-45)O

(45)O

Interlaminar

(45)O

(-45)O

Figure 11 Energy dissipation through dynamic deformation, fracture and friction of failed surfaces as a function

of time for the monolithic cylinder.

as fracture work. Figure 11(b) shows the energy

dissipated due to the creation of new crack surfaces

while Figure 11(c) shows energy dissipation due to

friction between failed surfaces.

Figure 12 shows the distributions of stress at

different times for a cylindrical sandwich composite

subjected to an underwater impulsive load. Initially,

the stress wave travels through the outer face,

creating highly stressed regions at the core-outer

face interface. The core undergoes significant

compression and minor cracking. Although large

scale delamination is caused due to the incident

loads, intralaminar cracking does not initiate. Due to

the absence of intralaminar cracking, there is no

structural rupture in spite of the reduction in overall

strength due to delamination. This indicates that in

addition to improve the overall stiffness of the

cylindrical structure, the PVC foam core also

improves blast mitigation by alleviating some of the

effects of flexural wave propagation in the

composite sections. For similar incident impulsive

loads, sandwich composites outperform monolithic

composite.

Figure 13 shows the time histories of displacement

and velocity for the inner and outer face of a

cylindrical sandwich composite structure subjected

to an impulsive load corresponding to V0 = 50m/s.

Initially, the core is compressed and the outer face

travels faster than the inner face. As deformation

progresses and the load is transmitted to the inner

face, the inner face acquires velocity and travels in a

direction opposite to the impulsive loading direction.

The evolution of elastic strain energy, fracture work

and frictional dissipation as functions of time is

shown in Figure 14. The energy expenditure in the

entire structure is shown in Figure 14(a). Elastic

strain energy is higher in the initial stages of

deformation. As damage initiates in the form of

delamination, intralaminar cracking and core

cracking, the magnitude of energy dissipated in

formation of cracks increases monotonically. With

an increase in overall fracture, the interactions

between fractured surfaces also increases leading to

high frictional dissipation. The fracture work and

frictional dissipation both surpass the elastic strain

energy. Figure 14(b) shows the energy dissipated

due to the creation of crack surfaces. The outer face,

which is in close proximity to the impulsive load,

undergoes the highest fracture work while the core

and inner face exhibit similar energy dissipation

characteristics. Figure 15 shows the time histories of

energy spent on creating cracks in different

9

RESPONSE OF CYLINDRICAL COMPOSITE STRUCTURES TO

UNDERWATER IMPULSIVE LOADING

components of the sandwich structure. Clearly,

damage initiation and growth is affected by material

orientation, interfacial effects and core cracking.

200 µs 400 µs

600 µs 800 µs

1000 µs 1200 µs

1400 µs 1600 µs

50

mm

σ (MPa)

400

350

300

250

200150

100

75

50

255

0

Figure 12 Distribution of stress at different times for a composite sandwich structure subjected to an underwater

impulsive wave.

0

10

20

30

40

50

60

70

0 100 200 300 400 500 600

Time (µs) Time (µs)

Ve

locity (m

/s)

0

5

10

15

20

25

30

35

0 100 200 300 400 500 600

Inner

face

Outer

face

Dis

pla

ce

me

nt (m

m)

Inner

face

Outer

face

Figure 13 Numerically calculated displacement and velocity as functions of time for the inner and outer faces of

a cylindrical sandwich composite structure subjected to an impulsive load corresponding to V0 = 50m/s.

THE 19TH

INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS

0

50

100

150

200

0 100 200 300 400 500 6000

50

100

150

200

0 100 200 300 400 500 600

Time (µs)

En

erg

y (J) Frictional

dissipation

En

erg

y (J)

Fracture

workStrain

energy

(a) Total

0

50

100

150

200

0 100 200 300 400 500 600

Time (µs)

En

erg

y (J)

Time (µs)

(b) Fracture work (c) Elastic strain energy

Total

Core

Outer

face

Inner

face

Total

Core

Outer

face

Inner

face

Figure 14 Energy dissipated in a cylindrical sandwich composite structure subjected to underwater impulsive

loading.

0

20

40

60

80

0 100 200 300 400 500 600

0

20

40

60

80

0 100 200 300 400 500 6000

20

40

60

80

0 100 200 300 400 500 600

En

erg

y (J)

En

erg

y (J)

En

erg

y (J)

Time (µs) Time (µs) Time (µs)

(a) Core (b) Inner face (b) Outer face

Total

Fracture

work

Interlaminar

Total

Interlaminar

(45)O

(-45)O(45)O

(-45)O

Figure 15 Fracture work in different components of a cylindrical sandwich composite structure subjected to

underwater impulsive loading.

0

50

100

150

200

250

300

0 100 200 300 400 500 600

0

50

100

150

200

250

300

0 100 200 300 400 500 600

Time (µs)

En

erg

y (J)

Frictional

dissipation

Fracture

work Strain

energy

Sandwich

Structure

Monolithic

Structure

Time (µs)

En

erg

y (J)

Total

Frictional

dissipation

Fracture

work

Strain

energy

Total

Figure 16 Comparison of total energy dissipation in monolithic and sandwich structures subjected to similar

impulsive loads.

6. Conclusion

The response of filament-wound cylindrical

composite structures is investigated numerically and

experimentally. The materials of choice are glass-

fiber reinforced polymer and structural PVC foam,

commonly found in marine construction.

Underwater impulsive loading experiments are

conducted at a fixed stand-off distance with

impulsive loads similar to those observed in an

underwater blast. Fluid-structure interaction is

captured using an equation of state for water. A

11

RESPONSE OF CYLINDRICAL COMPOSITE STRUCTURES TO

UNDERWATER IMPULSIVE LOADING

novel cohesive finite element framework is

implemented to accurately track the various

deformation mechanisms in composite structures.

This framework is able to accurately depict

interlaminar delamination and cracking, fiber and

matrix damage, intralaminar and translaminar

cracking and friction between newly created

surfaces.

Experiments show that monolithic and sandwich

composite structures exhibit multiple competing

failure modes include core compression,

delamination, core-face debonding, translaminar

cracking, matrix and fiber rupture. Maximum core

compression was observed on the side nearest to the

blast load, indicating that the outer face deformed

significantly into the core before recovering. For

similar total masses, the sandwich structure provided

considerably superior blast mitigation as compared

to the monolithic structure. Overall, filament wound

cylindrical structures exhibited good resiliency

under blast loading. While the monolithic structure

showed signs of severe internal damage and

warpage, the sandwich structure was relatively

unwarped and recovered most of the original

geometry.

Numerical simulations carried out in this analysis

provide an insight into the deformation mechanisms

and energy dissipation in the composite structures.

Simulations show that interlaminar delamination is

an important damage mechanism. Delamination

contributes to only 20% of the overall fracture work

and ~ 5% of total energy dissipation and it is the

driving force for other failure modes in the

composite. Delamination precipitates the formation

of intralaminar and translaminar cracks which lead

to catastrophic failure and rupture. Additionally,

interlaminar cracks span across large sections of the

composite while fiber and matrix cracking is

restricted to small regions close to the loading area.

Simulations reveal that friction between cracked

surfaces is major source of energy expenditure and

is comparable in magnitude to fracture work and

strain energy. Cracking and friction at the core face

interface is found to be negligible in all cases. This

can be attributed to the presence of the low density

foam core which does not provide a significant

resistance to shear deformation.

Computations reveal that cylindrical sandwich

structures outperform monolithic structures

significantly. The sandwich core helps mitigate the

effects of high pressures on the cylindrical structure.

Figure 16 shows a comparison of energy dissipation

in the form of fracture, friction and elastic strain.

Results indicate that for a similar applied impulse,

the sandwich structure dissipates almost twice as

much energy as the monolithic structure. This is

primarily because of the presence of a compressible

foam core and a thinner outer face which contribute

to higher elastic strain and fracture work

respectively.

The cohesive finite element model provides a unique

approach to track the different damage modes in

curved composites. Although the numerical model

captures the essential deformation mechanisms, it

slightly overestimates the effects of matrix cracking

and rupture. Therefore, the cohesive element

properties need to be recalibrated to ensure accurate

representation of experimentally observed failure

characteristics. Additionally, the effect of core

density on dynamic response of sandwich structures

is an important aspect that needs to be investigated.

The numerical capability can be utilized to design

and optimize curved fiber composite structures

subjected to side loading in navy vessels. In such an

approach, the newly developed numerical scheme

can provide an accurate and physically realistic

representation of experimental results. This

numerical scheme can be used for a variety of

materials and structural geometries.

6 Acknowledgements

The authors gratefully acknowledge support by the

Office of Naval Research (program manager: Dr.

Yapa D. S. Rajapakse).

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